separable
adjEtymology From Middle English separable, from Middle French separable and its etymon Latin sēparābilis.
7 senses
- 1Able to be separated.
- 2Able to be brought to a form where all occurrences of…
- 3Having a countable dense subset.
- 4Having no repeated roots (where roots are considered in…
- 5Such that none of the irreducible factors of P have a…
- 6Such that the minimal polynomial of every element of E…
- 7Satisfying any of several technical conditions on the…
Able to be separated.
Mathematics, Sciences Of a differential equation Able to be brought to a form where all occurrences of the dependent and the independent variable are on opposite sides of the equal sign.
Mathematical analysis, Mathematics, Sciences Of a topological space Having a countable dense subset.
› Any of several technical senses relating to…
Algebra, Mathematics, Sciences Of a polynomial Having no repeated roots (where roots are considered in an algebraic closure)
- x²#43;1 is separable, since its roots are i and -i.
› Any of several technical senses relating to… › Having no repeated roots (where roots are…
Algebra, Mathematics, Sciences Obsolete, Of a polynomial P, Of a polynomial Such that none of the irreducible factors of P have a repeated root.
› Any of several technical senses relating to…
Algebra, Mathematics, Sciences Such that the minimal polynomial of every element of E is a separable polynomial.
Of an algebraic field extension E/F
Algebra, Mathematics, Sciences Abstract Satisfying any of several technical conditions on the center of the algebra which generalize the situation of field extensions; see Separable algebra on Wikipedia.Wikipedia
Of an algebra over a ring
- Synonyms
- disunitable, separatable
- Antonyms
- annexable, combinable, inseparable
- Derived terms
- nonseparable, quasiseparable, semiseparable, separable affix, separable extension, separableness, separable polynomial, separable prefix, separable verb, separably, superseparable, unseparable
- Related terms
- separability